Some Results on Polish Groups

@article{Paolini2018SomeRO,
  title={Some Results on Polish Groups},
  author={Gianluca Paolini and S. Shelah},
  journal={arXiv: Logic},
  year={2018}
}
We prove that no quantifier-free formula in the language of group theory can define the $\aleph_1$-half graph in a Polish group, thus generalising some results from [6]. We then pose some questions on the space of groups of automorphisms of a given Borel complete class, and observe that this space must contain at least one uncountable group. Finally, we prove some results on the structure of the group of automorphisms of a locally finite group: firstly, we prove that it is not the case that… Expand

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